# Simulation of Rainfall-Runoff Process in a Catchment with a Check-Dam System Equipped with a Perforated Riser Principal Spillway on the Loess Plateau of China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Site and Data

#### 2.1. Study Area

^{2}with a main channel length of 3.75 km and an altitude ranging from 934.55 to 1187.75 m [28]. Loess soil is the most widely distributed soil in the studied catchment, with the characteristics of developed vertical joints, uniform particles, low clay content, and weak cementation between soil particles [29]. The average annual evaporation is 1519 mm, while the average yearly precipitation is 475.10 mm. Although precipitation varies yearly, it is distributed unevenly throughout the year. The rainfall from July to September accounts for 65% of the annual rainfall. Here, check dams are used as a key part of the management strategy to conserve soil and water. There are 23 check dams in the WMG catchment at present, and 16 of them can run normally with residual storage to trap sediments, and these 16 dams encompass 2 key check dams, 6 middle check dams and 8 small check dams, as shown in Figure 1b. Details of the check dam system are shown in Table 1.

#### 2.2. Data Sources and Processing

## 3. Method

#### 3.1. Discharge Capacity of the Perforated Riser Principal Spillway

^{3}/s; $c$ is the discharge coefficient; $\omega $ is the area of orifices; $g$ is the gravitational acceleration, m/s

^{2}; ${h}_{o}$ is the head over the centerline of the orifice, m; $L$ is the width of the rectangular orifice, m; and $d$ is the diameter of the riser pipe.

^{3}/s; $n$ is the row number of the orifices; and ${h}_{o}{}_{i}$ is the head over the centerline of the orifice in the $i$th row.

^{2}/s; $v$ is the mean velocity in the riser, m

^{2}/s; ${\zeta}_{e}$ is the entrance loss coefficient; $\lambda $ is the Darcy-Weisbach friction factor; $l$ is the length of the riser, m; ${\zeta}_{t}$ is the transition loss coefficient; ${l}_{b}$ is the length of the barrel, m; and ${d}_{b}$ is the inner diameter of the barrel, m.

#### 3.2. Modeling Approach

#### 3.2.1. Runoff Generation

#### 3.2.2. Direct Runoff

^{2}, and ${C}_{c}$ is the conversion constant, which is 2.08 in SI units.

#### 3.2.3. Runoff Concentration

^{3}/s; $x$ is the chainage, m; $A$ is the cross-sectional area, m

^{2}; $t$ is the time, s; ${q}_{in}$ is the lateral inflow, m

^{3}/s; $g$ is the gravitational acceleration, m/s

^{2}; $h$ is the water level, m; $C$ is the Chezy coefficient, m

^{0.5}/s; and $R$ is the hydraulic radius, m.

#### 3.3. Evaluation of Model Efficiency

^{2}), and Nash efficiency coefficient (NSE), with Equations (18)–(20) [37,38,39]:

^{3}/s, respectively, while ${S}_{i}$ and $\overline{S}$ are the simulated and average runoff, m

^{3}/s, respectively.

^{2}was to 1, the higher the degree of coincidence of the simulated runoff process. Moriasi, et al. [40] summarized that a simulated result could be considered perfect if its NSE equals 1, very good if its NSE falls between 0.75 and 1, good if NSE falls between 0.65 and 0.75, satisfactory if its NSE falls between 0.5 and 0.65 and unsatisfactory if the NSE is less than 0.5.

## 4. Results and Discussion

#### 4.1. Drainage Process of the Perforated Riser Principal Spillway

#### 4.2. Rainfall-Runoff Process in the Catchment

#### 4.2.1. Calibration and Sensitivity Analysis of the Model Parameters

^{2}and NSE were largest in scenario C1, and the difference between the simulated peak discharge and the observed data was smallest. The value of NSE at over 0.7 in the C1 scenario indicated that the model had good simulation accuracy and could simulate the change process of the flood well. Therefore, the values of $CN$ and the Manning coefficient in the C1 scenario were the most reasonable and can be used in the further simulation of the flood process in the catchment.

#### 4.2.2. Effects of Perforated Riser Principal Spillways on the Simulation Accuracy of Flood Processes

^{2}values of the 3 scenarios were all over 0.8, and the NSE values were all over 0.7, which indicated that the performances of the model under all 3 scenarios were good. The flood peak deviations of the 3 scenarios (the recommended formula scenario, technical code formula scenario and no drainage scenario) were 16.41%, 23.83% and 35.99%, respectively; in addition, for the recommended formula scenario, the simulation accuracy of the flood peak increased by 7.42% and 19.58% compared with accuracies of the technical code formula scenario and no drainage scenario, respectively. The R

^{2}and NSE values of the recommended formula scenario were slightly lower than those of the technical code formula scenario and no drainage scenario, which occurred mainly because the recommended formula scenario did not fit well in the small flow process of the flood retreating section. Considering that the discharge in the retreating section was far less than 1 m

^{3}/s and the flood risk of the check-dam system is mainly caused by the large floods during its operation, it is rational to improve the simulation accuracy of the flood peak with almost unchanged model accuracy using the recommended formula scenario.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Rainfall distribution process of the “7.26” rainstorm event at the Wangmaogou meteorological station.

No | Name | Subcatchment | Type | Height (m) | Storage Capacity (10^{4} m^{3}) | Residual Storage Capacity (10^{4} m^{3}) | Drainage Structure |
---|---|---|---|---|---|---|---|

1 | Wangtagou 2# | W1 | Small | 8 | 2.44 | 2.14 | |

2 | Wangtagou 1# | W1 | Small | 3.6 | 5.11 | 3.11 | |

3 | Sidizui 2# | W2 | Small | 20.8 | 15.8 | 5.87 | |

4 | Sidizui 1# | W2 | Middle | 14.1 | 5.07 | 0.19 | Perforated riser principal spillway |

5 | Guandigou 4# | W3 | Middle | 12.6 | 13.6 | 7.1 | Intake pipe on the slope |

6 | Guandigou 1# | W3 | Middle | 19.5 | 15.03 | 2.53 | Perforated riser principal spillway |

7 | Wangmaogou 2# | W4 | Key | 27.8 | 79.3 | 26.6 | Perforated riser principal spillway |

8 | Kanghegou 3# | W5 | Small | 12.3 | 8.34 | 5.84 | |

9 | Kanghegou 2# | W5 | Small | 18.2 | 11.5 | 7 | Perforated riser principal spillway |

10 | Nianyangou 4# | W6 | Small | 9.4 | 2.4 | 0.3 | |

11 | Nianyangou 3# | W6 | Small | 12.6 | 5.92 | 1.2 | |

12 | Nianyangou 2# | W6 | Middle | 9.4 | 4.2 | 0.2 | Intake pipe on the slope |

13 | Nianyangou 1# | W6 | Middle | 15.4 | 12.8 | 4.6 | Perforated riser principal spillway |

14 | Huangbaigou 2# | W8 | Small | 12.1 | 10.3 | 2.3 | |

15 | Huangbaigou 1# | W8 | Middle | 13.9 | 7.65 | 6.25 | Perforated riser principal spillway |

16 | Wangmaogou 1# | W9 | Key | 12.7 | 69.83 | 10.63 | Spillway |

Code | Land-Use | Area (km^{2}) | Proportion (%) |
---|---|---|---|

1 | Dam field | 0.50 | 8.67 |

2 | Rural land | 0.04 | 0.66 |

3 | Slope cropland | 0.89 | 15.38 |

4 | Transportation land | 0.05 | 0.86 |

5 | High coverage forestland | 0.02 | 0.28 |

6 | Medium coverage forestland | 0.60 | 10.37 |

7 | Low coverage forestland | 0.05 | 0.83 |

8 | High coverage grassland | 2.46 | 42.41 |

9 | Medium coverage grassland | 1.09 | 18.84 |

10 | Low coverage grassland | 0.10 | 1.70 |

Code | Subcatchment | Area (km ^{2}) | Length (km) | $\mathit{C}\mathit{N}$ | Standard Deviation | Slope (%) | Standard Deviation (%) |
---|---|---|---|---|---|---|---|

1 | W1 | 0.47 | 0.91 | 43.79 | 4.55 | 66.94 | 39.07 |

2 | W2 | 0.60 | 0.94 | 47.37 | 5.96 | 70.74 | 42.87 |

3 | W3 | 1.17 | 1.64 | 45.43 | 6.79 | 65.10 | 37.47 |

4 | W4 | 0.87 | 1.26 | 48.16 | 7.37 | 56.58 | 33.99 |

5 | W5 | 0.34 | 0.90 | 45.39 | 6.40 | 69.99 | 33.81 |

6 | W6 | 0.93 | 1.43 | 48.44 | 6.26 | 56.48 | 35.88 |

7 | W7 | 0.56 | 0.63 | 49.96 | 7.93 | 56.33 | 30.67 |

8 | W8 | 0.35 | 0.86 | 46.99 | 6.60 | 61.45 | 34.40 |

9 | W9 | 0.45 | 1.00 | 49.45 | 8.55 | 56.42 | 34.53 |

Parameter | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 |
---|---|---|---|---|---|---|---|---|---|

$CN$ | High | High | High | Medium | Medium | Medium | Low | Low | Low |

Manning coefficient | Low | Medium | High | Low | Medium | High | Low | Medium | High |

Scenario | R^{2} | NSE | Peak Discharge (m^{3}/s) | ||
---|---|---|---|---|---|

Obs. | Sim. | Difference (%) | |||

C1 | 0.818 | 0.734 | 24.26 | 20.28 | 16.41 |

C2 | 0.163 | 0.129 | 12.01 | 50.52 | |

C3 | 0.021 | −0.122 | 7.97 | 67.15 | |

C4 | 0.761 | 0.719 | 15.21 | 37.31 | |

C5 | 0.032 | −0.119 | 7.66 | 68.44 | |

C6 | 0.003 | −0.257 | 4.66 | 80.79 | |

C7 | 0.600 | 0.420 | 10.28 | 57.63 | |

C8 | 0.000 | −0.239 | 4.10 | 83.10 | |

C9 | 0.008 | −0.290 | 2.38 | 90.18 |

Scenarios | R^{2} | NSE | Peak Discharge (m^{3}/s) | ||
---|---|---|---|---|---|

Obs. | Sim. | Difference (%) | |||

Recommended formula scenario | 0.82 | 0.73 | 24.26 | 20.28 | 16.41 |

Technical code formula scenario | 0.83 | 0.78 | 18.48 | 23.83 | |

No drainage scenario | 0.87 | 0.83 | 15.53 | 35.99 |

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**MDPI and ACS Style**

Zhang, Z.; Chai, J.; Yuan, S.; Li, Z.; Xu, Z. Simulation of Rainfall-Runoff Process in a Catchment with a Check-Dam System Equipped with a Perforated Riser Principal Spillway on the Loess Plateau of China. *Water* **2021**, *13*, 2450.
https://doi.org/10.3390/w13172450

**AMA Style**

Zhang Z, Chai J, Yuan S, Li Z, Xu Z. Simulation of Rainfall-Runoff Process in a Catchment with a Check-Dam System Equipped with a Perforated Riser Principal Spillway on the Loess Plateau of China. *Water*. 2021; 13(17):2450.
https://doi.org/10.3390/w13172450

**Chicago/Turabian Style**

Zhang, Zeyu, Junrui Chai, Shuilong Yuan, Zhanbin Li, and Zengguang Xu. 2021. "Simulation of Rainfall-Runoff Process in a Catchment with a Check-Dam System Equipped with a Perforated Riser Principal Spillway on the Loess Plateau of China" *Water* 13, no. 17: 2450.
https://doi.org/10.3390/w13172450